Geometric sequences
(the database of solved problems)
All the problems and solutions shown below were generated using the Geometric sequences.
| ID |
Problem |
Count |
| 8951 | Find common ratio ( $ r $ ) in geometic progression if $ a_1 = \frac{ 1 }{ 64 } ~~ \text{and} ~~ a_{ 2 } = \frac{ 1 }{ 32 } $. | 1 |
| 8952 | Find $ a_8 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = -4 $. | 1 |
| 8953 | $$ a_1 = 5 ~,~ r = 2 ~,~ a_n = 9 ~,~ n = ? $$ | 1 |
| 8954 | $$ a_1 = \frac{ 1 }{ 64 } ~,~ r = 2 ~,~ a_n = 8 ~,~ n = ? $$ | 1 |
| 8955 | Find $ a_8 $ of a geometric progression if $ a_1 = \dfrac{ 1 }{ 64 } ~~ \text{and} ~~ r = -2 $. | 1 |
| 8956 | $$ a_1 = 1 ~,~ r = 3 ~,~ S_n = 19683 ~,~ n = ? $$ | 1 |
| 8957 | Find $ a_20 $ of a geometric progression if $ a_1 = 3906 ~~ \text{and} ~~ r = -\dfrac{ 4 }{ 5 } $. | 1 |
| 8958 | Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = -1 ~~ \text{and} ~~ r = 4 $. | 1 |
| 8959 | Find $ a_1 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 10 } ~~ \text{and} ~~ r = \dfrac{ 7 }{ 10 } $. | 1 |
| 8960 | Find $ a_2 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 10 } ~~ \text{and} ~~ r = \dfrac{ 7 }{ 10 } $. | 1 |
| 8961 | Find $ a_6 $ of a geometric progression if $ a_1 = 5000 ~~ \text{and} ~~ r = 1 $. | 1 |
| 8962 | Find $ a_6 $ of a geometric progression if $ a_1 = 20 ~~ \text{and} ~~ r = -4 $. | 1 |
| 8963 | Find $ a_3 $ of a geometric progression if $ a_1 = 27 ~~ \text{and} ~~ r = 9 $. | 1 |
| 8964 | Find $ a_2 $ of a geometric progression if $ a_1 = 18 ~~ \text{and} ~~ r = -6 $. | 1 |
| 8965 | Find $ a_9 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 6 }{ 5 } $. | 1 |
| 8966 | Find $ a_9 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = \dfrac{ 6 }{ 5 } $. | 1 |
| 8967 | Find $ a_5 $ of a geometric progression if $ a_1 = 7 ~~ \text{and} ~~ r = 10 $. | 1 |
| 8968 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 7 $. | 1 |
| 8969 | Find the sum of the first $ 240 $ terms of a geometric sequence if $ a_1 = 5000 ~~ \text{and} ~~ r = 1 $. | 1 |
| 8970 | $$ a_1 = 2 ~,~ r = 2 ~,~ S_n = 30 ~,~ n = ? $$ | 1 |
| 8971 | $$ a_1 = 2 ~,~ r = 2 ~,~ S_n = 250 ~,~ n = ? $$ | 1 |
| 8972 | $$ a_1 = 2 ~,~ r = 2 ~,~ S_n = 250 ~,~ n = ? $$ | 1 |
| 8973 | $$ a_1 = 2 ~,~ r = 2 ~,~ S_n = 256 ~,~ n = ? $$ | 1 |
| 8974 | Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 3 ~~ \text{and} ~~ r = \frac{ 4 }{ 5 } $. | 1 |
| 8975 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = -5 $. | 1 |
| 8976 | Find $ a_5 $ of a geometric progression if $ a_1 = \dfrac{ 9 }{ 25 } ~~ \text{and} ~~ r = \dfrac{ 5 }{ 3 } $. | 1 |
| 8977 | Find $ a_10 $ of a geometric progression if $ a_1 = \dfrac{ 125 }{ 9 } ~~ \text{and} ~~ r = -\dfrac{ 3 }{ 5 } $. | 1 |
| 8978 | Find $ a_9 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 10 } $. | 1 |
| 8979 | Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = 8 ~~ \text{and} ~~ r = -\frac{ 1 }{ 10 } $. | 1 |
| 8980 | Find $ a_9 $ of a geometric progression if $ a_1 = 8 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 10 } $. | 1 |
| 8981 | Find $ a_6 $ of a geometric progression if $ a_1 = 972 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 1 |
| 8982 | Find $ a_8 $ of a geometric progression if $ a_1 = 1536 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 8983 | Find $ a_12 $ of a geometric progression if $ a_1 = -5 ~~ \text{and} ~~ r = -3 $. | 1 |
| 8984 | Find $ a_9 $ of a geometric progression if $ a_1 = 125 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 5 } $. | 1 |
| 8985 | Find $ a_15 $ of a geometric progression if $ a_1 = 1 ~~ \text{and} ~~ r = 3 $. | 1 |
| 8986 | Find $ a_4 $ of a geometric progression if $ a_1 = 1600 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 4 } $. | 1 |
| 8987 | Find the sum of the first $ 50 $ terms of a geometric sequence if $ a_1 = -4 ~~ \text{and} ~~ r = 2 $. | 1 |
| 8988 | Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = -4 ~~ \text{and} ~~ r = -2 $. | 1 |
| 8989 | Find the sum of the first $ 79 $ terms of a geometric sequence if $ a_1 = \frac{ 99 }{ 100 } ~~ \text{and} ~~ r = 1 $. | 1 |
| 8990 | Find the sum of the first $ 80 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 0.99 $. | 1 |
| 8991 | Find $ a_7 $ of a geometric progression if $ a_1 = 6561 ~~ \text{and} ~~ r = \dfrac{ 3 }{ 10 } $. | 1 |
| 8992 | Find $ a_4 $ of a geometric progression if $ a_1 = 0 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 8993 | Find $ a_20 $ of a geometric progression if $ a_1 = 128 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $. | 1 |
| 8994 | Find $ a_4 $ of a geometric progression if $ a_1 = 200 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 5 } $. | 1 |
| 8995 | Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 1024 ~~ \text{and} ~~ r = 0.5 $. | 1 |
| 8996 | Find $ a_11 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = \dfrac{ 2 }{ 3 } $. | 1 |
| 8997 | Find $ a_5 $ of a geometric progression if $ a_1 = 13 ~~ \text{and} ~~ r = 5 $. | 1 |
| 8998 | Find $ a_7 $ of a geometric progression if $ a_1 = 243 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 3 } $. | 1 |
| 8999 | Find $ a_7 $ of a geometric progression if $ a_1 = 243 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 3 } $. | 1 |
| 9000 | Find $ a_6 $ of a geometric progression if $ a_1 = 5 ~~ \text{and} ~~ r = -3 $. | 1 |
